Problem: Solve for $x$ and $y$ using elimination. ${-2x-2y = -10}$ ${3x+5y = 19}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $2$ ${-10x-10y = -50}$ $6x+10y = 38$ Add the top and bottom equations together. $-4x = -12$ $\dfrac{-4x}{{-4}} = \dfrac{-12}{{-4}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-2x-2y = -10}\thinspace$ to find $y$ ${-2}{(3)}{ - 2y = -10}$ $-6-2y = -10$ $-6{+6} - 2y = -10{+6}$ $-2y = -4$ $\dfrac{-2y}{{-2}} = \dfrac{-4}{{-2}}$ ${y = 2}$ You can also plug ${x = 3}$ into $\thinspace {3x+5y = 19}\thinspace$ and get the same answer for $y$ : ${3}{(3)}{ + 5y = 19}$ ${y = 2}$